4. Reliability

The probability of successful packet reception is defined as reliability. In cyberphysical systems, particularly Smart Grid, wireless links may experience a great deal of challenges such as strong noise with heavy-tailed distributions. This means that reliability is a crucial parameter. There are three events in the transmission block, only one of which leads to successful transmission and others are failure events. As mentioned formerly, channel access failure and NO\_ACK in the last retransmission are responsible for the failure event.

$$R = \mathbf{1} - P\_{dc} - P\_{dr} \tag{43}$$

In which Pdc and Pdr are the probability of discarded packet (owing to channel access failure) and NO\_ACK in the last retransmission, respectively. Following the Markov model illustrated in Figure 5

$$P\_{dc} = \sum\_{j=0}^{n} \ge b\_{m, \, 0, j} = \frac{\varkappa^{m+1} (1 - \jmath^{n+1})}{1 - \jmath} \tag{44}$$

$$P\_{dr} = P\_c(\mathbf{1} - \boldsymbol{\beta}) \sum\_{i=0}^{m} b\_{i, -1, n} = \mathbf{y}^{n+1} \tag{45}$$
